JP4811567B2 - Stress measurement method for structures using photographed images - Google Patents

Description

The present invention relates to a stress measurement method that put the structure using the captured image.

  In recent years, there has been a movement to efficiently manage budgets by evaluating the soundness of structures such as bridges and implementing asset management. By the way, an important matter for evaluating the soundness of a structure is fatigue fracture. For example, in the case of a bridge, the fatigue failure occurs due to repeated running load of the vehicle, wind load, and other mechanical vibrations. In order to prevent this fatigue failure, it is important to grasp the stress concentration portion in the structure.

  Therefore, conventionally, the stress concentration degree is estimated by attaching a strain gauge to a portion where stress concentration may occur and measuring strain and displacement.

  In general, when a strain gauge is used, highly reliable strain data can be obtained, but only data on the pasting location and the pasting direction can be obtained.

  In particular, since the measured value is an average value of the gauge length, when the stress fluctuates greatly in a narrow range such as stress concentration, it was necessary to estimate by attaching many strain gauges. .

  By the way, research for detecting the stress generated in a structure not only at a position using a strain gauge but also from the entire field of view has been conducted. As one of the methods, there is a method using a photographed image photographed by a camera device. This method photographs images before and after a load is placed on a structure with the camera device, and determines the deformation amount of the structure on the load. This is obtained from the correlation between the captured images before and after placement (see, for example, Patent Document 1).

The method for obtaining the correlation from the images is to capture the state of the structure before the deformation or at a certain time as a “reference image”, and the state after the deformation or at the time of the inspection as a “measurement target image”. This method is used to determine the correlation between these two images. By using this method, it is possible to measure deformation in a wide range of areas that can be photographed with a camera device, and to improve the performance of recent digital cameras. In particular, the improvement in image resolution due to the increase in the number of pixels has made it possible to measure deformation with high accuracy. Has been done.
Japanese Patent Application Laid-Open No. 07-181075

However, as described above, the accuracy in obtaining the displacement amount using the correlation for the captured image by the camera device is determined by the number of pixels of the captured image, so-called resolution, and approaches the structure. However, there is a problem that the displacement cannot be measured accurately, that is, the stress cannot be measured accurately .

The present invention has an object to provide a put that stress measuring method in a structure using a photographic image that may seek accurately the amount of displacement of the structure.

In order to solve the above problems, a stress measurement method for a structure using a photographed image according to claim 1 of the present invention compares image information of the photographed image before and after applying force to the structure. A method for measuring stress by measuring the amount of displacement in the structure,
Using the Fourier transform method, the reference area part including the measurement target pixel and the measurement target area part that is a part related to measurement of the captured image after the force application are each related to the measurement of the captured image before the force application. Step to enlarge,
A step of obtaining a correlation amount by a residual sum of squares or normalization of image information of pixels in the enlarged reference area part and the measurement target area part while shifting the reference area part by one pixel from the measurement target area part. When,
A step of plotting the respective amount of correlation these obtained, corresponding to each pixel of the reference area portion on a flat surface,
Points representing respective amount of correlation is these plots or determining a song plane you pass near them,
And determining an extreme value of a song surface obtained by this step,
Determining the amount of displacement of the structure by determining the distance between the coordinate position of this extreme value and the coordinate position of the pixel of interest of measurement in the reference region portion of the photographed image before force application;
Substituting the displacement obtained in this step into the following equation (H1) to obtain strain;
Obtaining the stress generated in the structure based on the following equation (H2) represented by the strain obtained in this step and the coefficient matrix (quantity) including the longitudinal elastic modulus of the material of the structure. It is the method.

However, in the above formula, p _x And p _y Represents the length in the X-axis direction and the Y-axis direction of a rectangular element for stress analysis consisting of four measurement points, and u _i And v _i Represents the movement amount of the element in the X-axis direction and the Y-axis direction, and the element center (x + p _x / 2, y + p _y / 2) produces X-axis direction strain, Y-axis direction strain, shear strain, and X-axis direction stress, Y-axis direction stress, and shear stress, respectively _x , Ε _y , Γ _xy , And σ _x , Σ _y , Τ _xy Where E is the longitudinal elastic modulus of the measurement object, and ν is the Poisson's ratio.

According to the stress measurement method, the structure before and after applying force is photographed by the camera device, and the correlation amount of the image information in each pixel in the measurement target portion of both the photographed images is obtained. after obtaining the song plane you pass through the point or the vicinity thereof representing the correlation quantity, and position on the extreme preparative Ru flat surface in tracks face of this, the difference between the position of the measurement target pixel in the reference image Thus, the displacement amount for the position of the pixel to be measured can be accurately obtained within a range of, for example, one pixel or less, and the strain is obtained from this displacement amount. Since the stress generated in the structure is obtained based on the amount including the elastic coefficient, the stress generated in the structure can be obtained with high accuracy.

  That is, since the stress can be obtained from the photographed image of the structure, for example, the displacement amount, that is, the stress can be measured at any position without attaching a large number of strain gauges. Therefore, the structure can be managed with high accuracy, that is, efficient management can be performed.

[Embodiment]
Hereinafter, the stress measurement method that put the structure using the captured image according to an embodiment of the present invention, In detail, by measuring the displacement of the structure using the captured image, the stress of the structure A measuring method will be described with reference to the drawings.

First, a displacement amount measuring method in a structure , that is, a displacement amount measuring method will be described.

  In the present embodiment, in order to estimate the strength such as fatigue of a structure, a displacement amount (also referred to as a displacement amount) between before and after applying a load (force) is referred to as a camera device (for example, A digital video camera using a CCD is used), and the amount of displacement before and after that is obtained using pixel information, for example, luminance values, in the captured image before and after the application of the load.

  Here, a schematic configuration of an apparatus used for this displacement amount measuring method will be described.

  As shown in FIG. 1, the displacement measuring device includes at least a camera device 2 that is attached to a support base 1 and photographs a predetermined position of a structure, and a structure that is provided in the camera device 2 and is to be photographed. A distance measuring device 3 for measuring the distance of the camera, a laser irradiator 4 for irradiating a laser beam, for example, provided on the camera device 2 side to specify a photographing position, and a camera device for example provided on the support base 1 2, a GPS device 5 that measures the three-dimensional position, and a computer device (arithmetic device) 6 that calculates the displacement amount at the measurement target position in the structure by inputting measured values from the above-mentioned devices. Of course, the computer device 6 includes an input device 7 such as a tablet and a keyboard, and an output device such as a printer.

  Hereinafter, a method of measuring the displacement amount of the structure using the displacement amount measuring apparatus, that is, using a captured image will be described.

  First, the camera device 2 captures an image of the structure without applying a load to obtain an image before applying a load (hereinafter referred to as a reference image), and then images the structure with a load applied at a predetermined position. An image after applying a load (hereinafter referred to as a measurement target image) is obtained.

  Of course, at this time, the measurement data from the laser distance measuring device 3 and the GPS device 5 are used to accurately measure the position of the measured portion with respect to the camera device 2, and the displacement measuring device is based on these measured values. Correction or the like is performed so that the measured value obtained in step 1 becomes the correct displacement amount. In the following description, it is assumed that the measured displacement amount is corrected to a correct value.

  Next, by increasing the number of pixels in a portion (predetermined region) related to measurement in these two images, the measurement portion is expanded and the measurement accuracy of the displacement amount is improved.

  Hereinafter, an increase method (enlargement method) of the number of pixels will be described.

  For example, when there is an image having N × N pixels, if the width of the pixel is λ, the shooting area of this image is λN × λN.

  By the way, as shown in FIG. 2A, when the images having N × N pixels are each multiplied by M, that is, the number of pixels of MN × MN is as shown in FIG. In this case, the width λ ′ of each pixel is λ / M.

  On the other hand, when Fourier transform is performed on the image information (pixel value), that is, the luminance value of each increased pixel, a spatial frequency region as shown in FIG. 3 is obtained, and each side of the region is M times It will be done.

  Then, in this spatial frequency region, the luminance value in the range shown in FIG. 2A is made to correspond to the value obtained by performing the Fourier transform, but the actual data is the luminance value in the range of N × N. The Fourier transform value is only data in the range of −π / λ to π / λ (indicated by small points). Therefore, since the enlarged portion shown in FIG. 3 (the outer peripheral portion other than the small dot portion) does not have data, “0” is entered in this portion. That is, the window function for cutting the enlarged portion is used.

Next, when the inverse Fourier transform represented by the following equation (1) is performed on such a two-dimensional Fourier transform value a _kl , the number of pixels is multiplied by M × M (enlarged) image data A (m , N).

このようにフーリエ変換法による拡大方法を採用することにより、例えば周囲の４点の画素値を用いた補間法に比べて、１つの画素値を得るために、全てのフーリエ変換値（広範囲での値）が用いられることになり、したがってノイズの影響（悪影響）を少なくすることができる。

In this way, by adopting the enlargement method by the Fourier transform method, all the Fourier transform values (in a wide range) are obtained in order to obtain one pixel value, for example, as compared with the interpolation method using the surrounding four pixel values. Value) is used, and therefore the influence (adverse effect) of noise can be reduced.

  Next, a procedure for applying the image correlation method to the reference image and the measurement target image to obtain the displacement amount of the pixels based on the luminance value as image information will be described.

  In this procedure, the image correlation method is sequentially applied to a portion related to measurement for each predetermined pixel region (for example, a plurality of pixels). Here, the reference image side as a comparison source is referred to as the reference region. The measurement target image side to be compared is referred to as a measurement target region portion and will be described.

  That is, a method for obtaining a difference in luminance value (pixel value) of each pixel in the reference region portion and the measurement target region portion obtained by interpolating the luminance value for the pixel increased by the Fourier transform method as the number of pixels is increased will be described. To do.

  In the following description, in order to facilitate understanding, a one-dimensional rod-like body will be described as a structure.

  Furthermore, the number of pixel regions related to measurement is an odd number, for example, five, and a pixel that is focused on for measurement of displacement (hereinafter referred to as a measurement focused pixel) is a central pixel.

That is, as shown in FIG. 4A, the five pixel groups on the reference image side are made the reference area portion (A _i ), and the five pixel groups on the measurement target image side are made the measurement object region portion ( B _i ). Therefore, the central pixel (i-th pixel) is the measurement target pixel.

When comparing these two region portions (A _i , B _i ), first, as shown in FIG. 4B, one reference region portion (A _i ) is set to one side of the measurement target region portion (B _i ). In addition, for example, a residual sum of squares of luminance values (an example of a correlation amount) is obtained between the pixels in both region portions while being shifted by one pixel to the left. The residual sum of squares is obtained by adding the squares of the differences between the two luminance values and adding them for five pixels.

Then, the residual sum of squares is obtained for each of the residual area sums (A _i ) sequentially while shifting the reference area (A _i ) one pixel at a time (indicated by an arrow a).

Next, as shown in FIG. 4C, the position of the pixel to be measured in each moved reference area part A _i is set on the x axis, and each residual square obtained for each reference area part A _i is obtained. The sum (represented by the residual square sum correlation value r in the graph and indicated by a circle) is taken on the y-axis and plotted on the xy plane.

  Next, a quadratic curve (also referred to as a response curve) P passing through a plurality of plotted points or the vicinity thereof on the xy plane is obtained using a least square method. A polynomial curve, a sinc function curve, or the like can be used instead of the quadratic curve that is a response curve. Further, the steepest descent method may be used instead of the least square method.

Then, the extreme value of the quadratic curve P, in this case, the minimum x coordinate position (x _i ′) is obtained, and the x coordinate position and the measurement target pixel in the reference area A _i on the reference image are obtained. A difference from a certain center x-coordinate position (x _i ), that is, a deviation amount Δi is obtained.

  The obtained deviation amount is a displacement amount, and can be accurately measured as a so-called sub-pixel order displacement amount of one pixel or less.

Note that, on the right side of FIG. 4, the result {j-th pixel shift amount (Δj)} in the case where the same process as described above is performed in a different reference area A _j is shown.

By the way, in the above description, in order to facilitate understanding, the case of obtaining the displacement amount of the rod-shaped body has been described, but in the present embodiment, the flat plate constituting the surface (two-dimensional) of the structure, The amount of displacement is obtained.

  In this case, the reference area portion and the measurement target area portion are naturally planes, and a residual square sum (or residual square sum correlation value) for each pixel in these two-dimensional planes is obtained.

  Then, for example, a quadric surface (also referred to as a response surface) represented by the following equation (2) that can pass through each point of the residual sum of squares is obtained by the least square method, and an extreme value on the curved surface, for example, a minimum value The point on the plane becomes the position where the measurement pixel of interest in the reference area on the reference image has moved, and this moving distance is the amount of displacement. Note that a curved surface represented by a polynomial, a curved surface represented by a sinc function, or the like can be used instead of a quadric surface that is a response surface. In this case, the steepest descent method may be used instead of the least square method.

図５に、この二次曲面Ｓを示しておく。但し、相関値にて表されている。

FIG. 5 shows this quadric surface S. However, it is represented by a correlation value.

  Here, the experimental result using the displacement amount measuring method according to the present invention is shown in FIG.

  FIG. 6 shows a measured value by a displacement measuring method according to the present invention and a measured value by a strain gauge when a tensile load is applied to a rectangular plate (2 t × 30 W × 300 L; unit is mm) as a test piece. Comparison with is shown. In addition, (a) is the graph which compared the measured value, (b) is a figure which shows the external appearance of a test piece. Moreover, the measured value of the displacement amount by the strain gauge shown in FIG. 6A is obtained by integrating the strain amount obtained from the strain gauge.

  From the results shown in FIG. 6, it can be seen that the measurement value obtained by the displacement amount measuring method according to the present invention is substantially equivalent to the measurement value obtained by the strain gauge. From this, it was found that the displacement amount (deformation amount) of the structure can be measured with high accuracy without using a strain gauge by using the displacement amount measuring method according to the present invention.

  The displacement measurement method according to the present invention, unlike the measurement method using the strain gauge, enables measurement of the displacement over almost the entire surface of the image capturing region. This is a very effective method.

  As described above, the structure before and after applying the load is imaged with the camera device, and after the enlargement process is performed on the portion related to the measurement of both the captured images, in these enlarged areas, After obtaining the residual sum of squares of the luminance value in each pixel in the measurement target portion, and obtaining a curved surface passing through the point representing the residual sum of squares or the vicinity thereof by the least square method, the extrema on the curved surface, for example, Since the difference between the position on the plane that takes the minimum value and the position of the measurement target pixel in the reference image is obtained, the displacement amount for the position of the measurement target pixel is within one pixel or less, that is, the sub Therefore, the displacement amount of the structure, that is, the deformation amount can be obtained with high accuracy.

  Next, a stress measurement method using the displacement amount measurement method will be briefly described.

  Based on the displacement amount accurately obtained by the displacement amount measuring method, that is, as shown in the following formulas (3) and (4), an amount representing the relationship between the displacement amount (δ) and the displacement-strain ( For example, a strain (ε) is calculated from the coefficient matrix (B) and a quantity representing a stress-strain relationship (for example, a coefficient matrix including a longitudinal elastic modulus of a material constituting the structure). ) By multiplying [D], the stress (σ) generated in the structure can be obtained. That is, since the stress can be obtained from an image obtained by photographing the structure, for example, the displacement amount, that is, the stress can be measured without attaching a large number of strain gauges and at any position. Since the place where it has occurred can be grasped easily and accurately, the structure can be managed with high accuracy, that is, efficient management can be performed.

勿論、上述した変位量を求める演算およびこの変位量に基づく応力の演算（解析）については、コンピュータ装置に具備された演算用プログラムにより行われる。

Of course, the calculation for obtaining the displacement amount and the calculation (analysis) of the stress based on the displacement amount are performed by a calculation program provided in the computer apparatus.

  Here, a method for calculating the stress using the displacement measurement value obtained by the above-described method will be specifically described.

That is, with respect to the measurement point N ₀₁ (x, y) in the reference image, adjacent measurement points in the X-axis direction and the Y-axis direction are represented by N ₀₂ (x + p _x , y), N ₀₄ (x, y + _py ). In addition, when the measurement point on the diagonal is considered as N ₀₃ (x + p _x , y + _py ), the stress analysis can be performed by an element including these four measurement points. In this case, the elements in the reference image, the length in the X-axis direction is considered as a square p _x, the length in the Y axis direction is p _y. Then, it is considered that these four deformation measurement points N _0i (i = 1 to 4) have moved u _i and v _{i in} the X-axis direction and the Y-axis direction, respectively. At this time, the element center point N ₀ (x + p _x / 2, y + p _y / 2) composed of these four measurement points is generated after deformation in the X-axis direction strain, the Y-axis direction strain, the shear strain, and the X-axis direction stress, the Y-axis. The directional stress and shear stress are respectively expressed as ε _x (x + p _x / 2, y + p _y / 2), ε _y (x + p _x / 2, y + p _y / 2), γ _xy (x + p _x / 2, y + p _y / 2), respectively. And σ _x (x + p _x / 2, y + p _y / 2), σ _y (x + p _x / 2, y + p _y / 2), τ _xy (x + p _x / 2, y + p _y / 2), these values are It can be simply obtained from the following equations (5) and (6).

上記（６）式中、Ｅは測定対象物の縦弾性係数、νはポアソン比である。

In the above equation (6), E is the longitudinal elastic modulus of the measurement object, and ν is the Poisson's ratio.

  That is, by using the above equation, stress analysis can be performed based on the displacement measurement value at the subpixel level.

Here, experimental results using the stress measurement method based on the displacement according to the present invention will be shown.

  FIG. 7 is a view of a test piece in which a circular hole (hole diameter is 10 mm) is formed in a rectangular plate (2t × 30W × 300L; unit is mm), and FIG. 8 is a tensile load applied to the test piece. FIG. 9 is a diagram showing the stress distribution of the entire measurement region obtained based on the displacement obtained by the displacement measurement method according to the present invention, and FIG. 9 shows the stress obtained by the stress measurement method according to the present invention. It is the figure which compared distribution (shown with a continuous line), the stress (shown with a plot location) measured with the strain gauge, and the theoretical value (shown with a broken line) shown to following (7) Formula. In FIG. 8, three cases 1 to 3 having different tensile loads are shown. Further, FIG. 8 shows that stress concentration occurs at the side of the circular hole, and stress decreases at the upper and lower parts of the circular hole. In addition, from FIG. 9, there is some difference on the left side of the circular hole, but overall, the results of the measured values by the subpixel image processing, the measured values by the strain gauge, and the theoretical values are almost the same. It turns out that it is.

上記（７）式中、σ_０は円孔中心から上部７５ｍｍの位置にあるひずみゲージから計算した円孔遠方部での応力値（図７の二点鎖線にて示す）であり、ｒは円孔の半径であり、ｘは円孔中心からの位置（距離）を示す。

In the above equation (7), σ ₀ is the stress value (indicated by the two-dot chain line in FIG. 7) at the far hole of the circular hole calculated from the strain gauge located 75 mm above the circular hole center, and r is the circle The radius of the hole, and x indicates the position (distance) from the center of the circular hole.

  Further, hereinafter, the displacement amount measuring method according to the above-described embodiment will be described in a step format.

That is, the displacement amount measuring method according to the above embodiment is a method for measuring the displacement amount in the structure by comparing the image information of the captured images before and after applying force to the structure. Then, a Fourier transform method is used to calculate a reference region portion including a measurement target pixel and a measurement target region portion that is a portion related to measurement of a captured image after the force is applied. Each of the enlarged reference region portion and the measurement target region portion, image information between pixels in the enlarged reference region portion and the measurement target region portion, for example, a residual sum of squares of luminance values or a correlation amount by normalization, and the reference region portion as the measurement target region portion. a step of plotting and determining shifting by one pixel, each correlation amounts thereof obtained, corresponding to each pixel of the reference area portion on a flat surface with respect to these Determining a tune surface you pass through the point or in the vicinity thereof representing respective correlation amount which is lot, and determining an extreme value of a song surface obtained by this step, the coordinate position of the extreme value, the force imparted before And obtaining a displacement amount of the structure by obtaining a distance from the coordinate position of the measurement target pixel in the reference region portion of the captured image.

  In addition, the stress measurement method simply calculates a strain from the displacement obtained by the displacement measurement method, and based on the strain and the amount including the longitudinal elastic modulus of the material of the structure, the structure This is a method for obtaining the stress generated in the.

The configuration of the stress measuring device according to the present embodiment has the following effects.
(1) By integrating the camera device, the computer device for displacement and stress analysis, and the output device, the stress state of the structure at the site can be immediately evaluated, so the inspection and diagnosis of the structure can be performed efficiently. Can be implemented.
(2) Since the laser distance measuring device and the GPS device incorporated in the stress measuring device can efficiently acquire the position information of the measured portion, data analysis and structural soundness diagnosis are easily performed. be able to.
(3) applying deviation using response surface position, that is, was to seek the displacement amount, the displacement to be measured in 20nm accuracy of about, thus to the field of stress measurement which can not be conventionally camera system can do.
(4) By combining the image enlarging method and the response surface method, it is possible to improve the accuracy of strain detection, and consequently improve the accuracy of stress measurement.

  In the above embodiment, the residual sum of squares (residual sum of squares correlation value) is used as the image correlation method (correlation amount) for obtaining the displacement amount between pixels. For example, a normalized correlation value may be used. it can.

  When obtaining a normalized correlation value, the following equation (8) (in the case of a quadric surface) is used.

また、上記実施の形態においては、計測に係る部分の撮影画像を、フーリエ変換法を用いて拡大するように説明したが、場合によっては、拡大しなくても、二次曲面の極値を求めることにより、やはり、変位量を精度良く求めることができる。

In the above-described embodiment, the captured image of the portion related to the measurement has been described as being enlarged using the Fourier transform method. However, in some cases, the extreme value of the quadric surface is obtained without being enlarged. As a result, the amount of displacement can be determined with high accuracy.

It is a side view which shows schematic structure of the apparatus for enforcing the stress measuring method by the displacement amount which concerns on embodiment of this invention. It is a figure for demonstrating the expansion method of the image area at the time of measuring the displacement amount, (a) shows the image area before expansion, (b) shows the image area after expansion. It is a figure which shows the spatial frequency area expanded by the expansion method. A diagram for explaining the total measuring method of the amount of displacement, (a) shows the image area, (b) shows a comparison method shows the correlation values (c) is the residual sum of squares. A diagram for explaining the total measuring method of the amount of displacement is a perspective view showing a correlation value of the residual sum of squares in plan. A diagram showing experimental results of a total measuring method of the amount of displacement, (a) shows the graph showing the comparison of the measured values, indicating the appearance of (b) was used in the experiment the test piece. A view showing an external appearance of the test piece according to another experiment with total measuring method of the amount of displacement, (a) shows the overall view, an enlarged view of (b) the measurement target region. It is a top view which shows the stress distribution in the other experimental result. It is a graph which shows the comparison with the measured value and the theoretical value by the stress value in another experimental result, and a strain gauge.

DESCRIPTION OF SYMBOLS 1 Support stand 2 Camera apparatus 3 Laser ranging apparatus 4 Laser irradiator 5 GPS apparatus 6 Computer apparatus

Claims (1)

A method of measuring stress by measuring the amount of displacement in the structure by comparing the image information of the captured image before and after applying force to the structure,
Using the Fourier transform method, the reference area part including the measurement target pixel and the measurement target area part that is a part related to measurement of the captured image after the force application are each related to the measurement of the captured image before the force application. Step to enlarge,
A step of obtaining a correlation amount by a residual sum of squares or normalization of image information of pixels in the enlarged reference area part and the measurement target area part while shifting the reference area part by one pixel from the measurement target area part. When,
A step of plotting the respective amount of correlation these obtained, corresponding to each pixel of the reference area portion on a flat surface,
Points representing respective amount of correlation is these plots or determining a song plane you pass near them,
And determining an extreme value of a song surface obtained by this step,
Determining the amount of displacement of the structure by determining the distance between the coordinate position of this extreme value and the coordinate position of the pixel of interest of measurement in the reference region portion of the photographed image before force application;
Substituting the displacement obtained in this step into the following equation (H1) to obtain strain;
The step of determining the stress generated in the structure based on the following equation (H2) expressed by the strain obtained in this step and the coefficient matrix including the longitudinal elastic modulus of the material of the structure: A stress measurement method for a structure using a characteristic photographed image.

However, in the above formula, p _x and p _y represents the length of the X-axis direction and the Y-axis direction of the rectangular element for stress analysis of four measurement points, u _i and v _i are the elements X This represents the amount of movement in the axial direction and the Y-axis direction. X-axis direction strain, Y-axis direction strain, shear strain, and X-axis direction stress generated after the element center (x + p _x / 2, y + p _y / 2) is deformed, Y The axial stress and shear stress are ε _x , ε _y , γ _xy , and σ _x , σ _y , τ _xy , respectively, E is the longitudinal elastic modulus of the measurement object, and ν is the Poisson's ratio.

Images